Two prominent Republicans with thinly-veiled presidential ambitions – former House speaker Newt Gingrich and former Florida Governor Jeb Bush – have recently announced major new publicity campaigns aimed at capturing Latino voters for the GOP. Last weekend, Gingrich's new web-based political organisation, "Americanos", hosted a two-day summit in Washington, DC to discuss how the GOP might capitalise on its recent midterm Latino successes – in part, by embracing a conservative version of the "comprehensive immigration reform" agenda that Democrats have long championed.

And Bush, a party centrist considered the GOP's chief emissary to America's Latino communities, plans to follow up the Gingrich event with a major appearance of his own at the January 2011 kickoff of the American Action Forum (AAF), a national advocacy group funded by the same close-knit group of Texas millionaires that backed Bush's younger brother for president in 2000. AAF also lists powerful GOP operative Karl Rove, who helped direct the Bush presidency, and former Minnesota Senator Norm Coleman, a GOP moderate who backed comprehensive immigration reform in 2006 and 2007, as its co-founders and chief operating officers.

With the Latino share of the US electorate continuing to rise, is it any surprise that top Republicans would be targeting America's largest and fastest-growing ethnic group?

Hardly. But the latest efforts by Gingrich and Bush also reflect a determination by some of the party's most senior strategists to defuse the far right's hardline nativism and to steer the party back to the softer "family-and-faith" conservatism that worked so well for George Bush in 2000, and especially in 2004, when he captured a unprecedented 44% share of the Latino vote.

In fact, Republicans remain divided on how to interpret the recent mid-term election results. On the one hand, notwithstanding its growing reputation for "nativism", exit polls suggest that the GOP gained close to 40% of the Latino vote, up from just 30% in the midterm elections in 2006, an enormous gain. And the party fielded its largest crop of Latino candidates ever, including Marco Rubio and Susana Martinez, who captured a key Senate seat in Florida and the governor's mansion in New Mexico, respectively. Both candidates, and five other GOP Latinos who won House seats, attacked the Democrats' "amnesty" proposals and embraced Arizona's harsh new enforcement law – and yet, each managed to capture a significant share of Latino voters (55%, in the case of Rubio), while pulling in most whites, too.

Despite these successes, Gingrich and Bush are clearly concerned that most GOP candidates in the future won't have the advantage of shared ethnicity to make up for lingering Latino suspicion towards the GOP. And clearly, that suspicion was on full display in key battleground states out west. GOP Senate candidates in Nevada (Sharron Angle), California (Carly Fiorina) and Colorado (Ken Buck) who espoused or abetted hard-line stances on illegal immigration ended up losing their midterm races, largely because of a surge of Latino support for their Democratic rivals.

And with 23 Senate Democrats up for re-election in 2012, compared to just 10 Republicans, GOP moderates don't want immigration politics to stand in the way of a renewed effort to capture the Senate, to say nothing of the presidency, at a time when so many voters, including Latinos, are becoming more open to GOP ideas on jobs and the economy.

Gingrich, for one, is not shy about criticising Republican insensitivity to immigrants, or about promoting a still-to-be-defined version of "comprehensive immigration reform" that would include at least a partial legalisation programme ("We can't deport everybody," he says). And he's spent months learning conversational Spanish so that he can beginning addressing his Latino audiences in both languages. Latinos seeking something more than the usual "mariachi politics" – or token outreach – from the two parties are likely to respond warmly to that gesture, and to Gingrich's moderation generally, as they did to George Bush. While he's yet to be tested on the stump, Gingrich is clearly on the right track.

One big question, though, is how the party, including future presidential candidates, will fare if the GOP far right gains significant new influence in the 112th Congress and continues to fan the flames of nativism. The two most important House leadership positions on immigration – the judiciary committee, and its immigration subcommitte – are slated to be filled by hardliners Lamar Smith and Steven King. Both men are planning to introduce legislation to repeal "birthright" citizenship for illegal immigrant children, which has been sacrosanct for decades.

Even long-time immigration conservatives like Mark Krikorian of the Centre for Immigration Studies, which advocates a reduction of both legal and illegal immigration, opposes the repeal push on the grounds that it will distract the country from more pressing improvements in immigration enforcement at the border and the workplace.

So worried are some Hispanic Republican business leaders about the expected Smith-King immigration offensive that they recently sent a letter to GOP party leaders, including current minority leader Mitch McConnell, urging them to assign the open leadership posts to other Republicans. McConnell has yet to respond to their letter.

Meanwhile, among Democrats, the midterm voting results, and the continuing obstacles to immigration reform, are provoking potentially explosive internal divisions between the party leadership and its Latino base. A chorus of Latino Democrats, led by Representative Luis Gutierrez of Illinois, the leading supporter of comprehensive immigration reform in the House, is threatening to "take it to the streets", if majority leader Harry Reid, one of the senators who owes his narrow re-election to Latinos, fails to convince Congress this week to pass the partial legalisation bill known as the "Dream Act".

The measure, which would legalise some 2 million children of illegal immigrants who moved to the US with their parents through "no fault of their own", is considered a minimal downpayment on the sweeping legalisation programme that Obama promised immigration activists he would promote when he took office two years ago. But despite Obama's continuing verbal support – some would say, lip service – the president still hasn't taken strong and visible leadership on the issue, leaving Congress deadlocked and activists incensed.

All of which only makes Gingrich's outreach initiative for the Republican party, notwithstanding its own divisions on immigration, all the more astute and well-timed.